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  • 1
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    A simplified algorithm for correcting both errors and erasures of R-S codes (1978)
    In:  CASI
    Details
    Publication Date: 2006-01-12
    Description: Using the finite field transform and continued fractions, a simplified algorithm for decoding Reed-Solomon (R-S) codes is developed to correct erasures caused by other codes as well as errors over the finite field GF (q(m), where q is a prime and m is an integer. Such an R-S decoder can be faster and simpler than a decoder that uses more conventional methods.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Deep Space Network; p 66-71
    Format: text
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  • 2
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    A new algorithm for computing primitive elements in GF q square (1978)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: A new method is developed to find primitive elements in the Galois field of sq q elements GF(sqq), where q is a Mersenne prime. Such primitive elements are needed to implement transforms over GF(sq q).
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Deep Space Network; p 190-196
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  • 3
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    The fast decoding of Reed-Solomon codes using high-radix fermat theoretic transforms (1976)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Deep Space Network; p 75-80
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  • 4
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    The fast decoding of Reed-Solomon codes using fermat theoretic transforms and continued fractions (1976)
    In:  Other Sources
    Details
    Publication Date: 2011-08-17
    Description: It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform algorithm over finite fields GF(F sub n) where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Deep Space Network; p 63-74
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  • 5
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    A new fast algorithm for computing a complex number: Theoretic transforms (1977)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: A high-radix fast Fourier transformation (FFT) algorithm for computing transforms over GF(sq q), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Deep Space Network, Vol. 39; p 71-75
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  • 6
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    Decoding of 1/2-rate (24,12) Golay codes (1989)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A decoding method for a (23,12) Golay code is extended to the important 1/2-rate (24,12) Golay code so that three errors can be corrected and four errors can be detected. It is shown that the method can be extended to any decoding method which can correct three errors in the (23,12) Golay code.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Telecommunications and Data Acquisition Report; p 202-207
    Format: application/pdf
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  • 7
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    Simplified Syndrome Decoding of (n, 1) Convolutional Codes (1983)
    In:  CASI
    Details
    Publication Date: 2014-09-10
    Description: A new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck is presented. The new algorithm uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). This set of Diophantine solutions is a coset of the CC space. A recursive or Viterbi-like algorithm is developed to find the minimum weight error vector cirumflex E(D) in this error coset. An example illustrating the new decoding algorithm is given for the binary nonsymmetric (2,1)CC.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Telecommun. and Data Acquisition Rept.; p 15-21
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  • 8
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    A decoding failure test for the transform decoder of Reed-Solomon code (1981)
    In:  Other Sources
    Details
    Publication Date: 2011-08-18
    Description: Using a finite field transform, a transform decoding algorithm is able to correct erasures as well as errors of any (n,k,d) Reed-Solomon code over the finite field GF(q). A pitfall of transform decoding and how to avoid it are discussed. A simple test is given so that the decoder fails to decode instead of introducing additional errors, whenever the received word contains too many errors and erasures.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: Telecommun. and Data Acquisition; p 121-124
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  • 9
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    A VLSI architecture of a binary updown counter (1987)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A pipeline binary updown counter with many bits is developed which can be used in a variety of applications. One such application includes the design of a digital correlator for very long baseline interferometry (VLBI). The advantage of the presently conceived approach over the previous techniques is that the number of logic operations involved in the design of the binary updown counter can be reduced substantially. The architecture design using these methods is regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Telecommunications and Data Acquisition Report; p 52-58
    Format: application/pdf
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  • 10
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    Error-trellis Syndrome Decoding Techniques for Convolutional Codes (1984)
    In:  CASI
    Details
    Publication Date: 2014-09-12
    Description: An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decoding is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: The Telecommun. and Data Acquisition Rept.; p 122-134
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